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Example 1 (Divide-and-choose) Situation: A mother buys a cake for her son and daughter, who love cakes so much ! Rule : the daughter cuts the cake first, then the son chooses the part he wants to have.

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Example 1 (Divide-and-choose) Assume the daughter has two strategies: 1, cut it into half 2, cut it into one-fourth and three-fourth The son has two strategies: 1, choose the larger one 2, choose the smaller one

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Example 3 (grading scheme) Situation: In MATH 162, students have the chance to give marks to other students, which will affect the course grade. Rule: Prof. Li chooses the grading scheme first. Students then choose whether they will intentionally give low marks.

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Let’s play a game! I have a 10 dollars notes The first player proposes a method on how to divide it. e.g. 1, I get all 10 dollars, you get nothing I give you all 10 dollars, I get nothing

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Let’s play a game! The second player can choose whether to accept or not. - If he accepts, we will divide the 10 dollars note as proposed by first player. - If he turns down, none of them get anything.

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Let’s play a game! On a paper, write down: 1, if you are player 1, what will you propose. 2, if you are player 2, the minimum amount that you need to get in order to accept player 1‘s offer

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Let’s play a game! What should be the solution? Famous game: Ultimatum game

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Homework 1, Solve the divide-and-choose game when the daughter can choose to divide in any proportion she likes. You can consider the two strategies to be: divide equally and divide unequally 2, Solve the Ultimatum game. You can consider the strategies of player 1 to be: player 1 get all, player 1 get $9.9 and player 1 get less than $9.9

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Homework (Extra) Andy, Ben, Charles are in a one-round three-way duel. They take turn shoot at each other or fire up in the air. They never miss a shoot. Andy start first, followed by Ben and Charles. They want to be the sole survivor and never want to die. Show that Andy will fire up in the air. [Hint: backward reasoning makes things complicated this time]

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Discussion 1, Do you find game theory interesting? 2, Have you used backward reasoning in daily life? 3, In Ultimatum game, players usually do not play the solution at first. Can you suggest some reasons?